Numerals.. or absence thereof

Anyone curious about why the “…Greater Khorasan” series hasn’t resumed yet – the publishers-that-be decided to send me a certain book by sea. I’m  to expect it soon..  how soon? …oh, sometime in  January or perhaps  February… but very soon. 🙂

Meanwhile, some musing and notes about number.

There is a mathematical text in manuscript which nicely connects with a number of our present themes:  Iberia under Muslim rule; manuscripts in Pennsylvania University’s  LJS (Lawrence J. Shoenberg) collection;  the vexed question of numerals and their presence or absence in the Voynich manuscript; the astronomical works of al-Tusi, a native of greater Khorasan; distinction between age and sources for images as against those for accompanying written text – and of course the copying of manuscripts in Baghdad.

The manuscript which does all – or most – of this is LJS 293 –  made in  twelfth century Baghdad, and once owned by THE Naṣīr al-Dīn Muḥammad ibn Muḥammad al-Ṭūsī, himself [1] ~ the text having been composed  in the Maghreb or in al-Andalus by one  Abū Bakr al-Ḥaṣṣār. Paul Kunitzsch dates the LJS copy  to 1174; the holding library gives 1194 AD.

“Hindu-Arabic numerals…”

The text is known as  ‘Kitāb al-Bayān wa al-tidhkār fī sanʻat ʻamal al-ghubār‘ and this particular copy  is the earliest of the five copies known to be  extant.  On folio 4r, we see the Hindu-Arabic numerals  shown in both the  western and the eastern Islamic form.

altusi-numerals-eastern-and-western-arabicThe full catalogue entry can be read on the “Penn in hand” website here.

Paul Kunitzsch’s discussion of it was given in a paper  delivered in 2002, subsquently filled out and published in 2003.[2]  His comments focus on the manuscript’s importance given a general paucity of evidence for the numerals’ forms in western Arabic sources earlier than  c.1400.

Not that there can be any doubt that the Hindu-Arabic numerals themselves were known in western Islamic regions as early as the tenth century, for in connection with another work I’ve mentioned here recently,  The Book of Creation (Sefer Yetzira), a tenth-century commentary mentions the Hindu numerals and the fact that the author of the commentary had already written a monograph on the subject.

Just  forty years after (and thus still during the tenth century),  knowledge of the Hindu-Arabic numerals had passed to the Latins (Mozarabs) of al-Andalus,  after which time  it would continue (to use  Kunitzsch’s words)  as  “a rich tradition in Latin works on the abacus”.  In this the Jewish community continued an active presence  and, as  Kunitzsch also notes,  al-Ḥaṣṣār’s mathematical text would be translated into Hebrew in  Al-Andalus in 1271, by Moses ibn Tibbon.

Another Iberian Jewish manuscript, this now in the LJS collection, was made late in the fourteenth century, and reminds us that even when a text may be fairly recent, the images need not.   It is also largely concerned with maths, but the mathematics of astronomy.  It includes an image for Gemini with figures drawn in a very similar style to some of the ‘nymphs’ in the Voynich manuscript.  While the text on that page comes from current calculations for the appropriate latitude,  the imagery derives from a non-Latin tradition derived from the tenth-century astronomer  al-Sufi (903-986 AD).   This manuscript is Sassoon 823,  catalogued at UPenn as  MS LJS 057. [3]

sassoon-gemini-ljs-o57-p-125To make everything neat, or perhaps confuse it utterly, a compilation of texts by authors who are called “al-Maghrebi” and “al-Iraki”, said to be on fourteenth century alchemical works  but itself dated to the 18thC by the holding library, contains Voynich-like glyphs (below, detail A)  So does another, known as the Book of Surprises (detail B).  Are they meant for numerals? No-one knows.

scripts-voynich-like

 

“.. or lack of them..”

If  I am correct in thinking that the content embodied in the Voynich manuscript is not derived from a standard textbook, and is not of  Latin Christian authorship, but is a compilation of practical and technical matter related to the east-to-west trade, then the text’s apparent lack of secretarial hand and of Hindu-Arabic (or Latin) numerals need not cause quite so much concern, for the forms and language of  business documents are a separate class of writing, even in the fourteenth century.  Below, as example, an illustrated invoice made by a fourteenth century Italian who lived for years in Avignon, engaged regularly with the Jews and had business interests in the Maghreb.[4]

Datini detail

 

To explain why texts related to business might include no  form of numeral, or very few, I’ll refer to Eva Mira Grob’s  work.  She has transcribed, translated and commented on business letters which were written on papyrus,  and which date from the 3rdC – 10thC AD. [5].

In one place, she writes:

Enumerations in the form of lists are not integrated into the text. The common way is to include all … information … as a running text without any special graphical marking and to write numerals in words. Clarity is achieved by repetitive linguistic patterns.

A great deal has been written and said about the Voynich manuscript’s text and its repetitive patterns, but for newcomers who may be especially interested in this,  I’d suggest consulting first a couple of specialist blogs by statisticians and linguists: among them those by Julian Bunn and  Emma May Smith. If  linguistics is your specialty –  not just a casual interest –  then of course you cannot ignore the substantial body of  work done by earlier specialists. In particular, the data compiled by Georg Jorge Stolfi (sorry) should be considered, for he concluded from it that the text must have been written in a non-Indo-European language.

Below is a passage from one letter as transcribed and translated by Grob, illustrating those points about itemised lists and  repetitive linguistic patterns. (you can click on the image to enlarge it further).

grob-quote

so.. what if these ‘vords’ are numbers and markers of dinars?  or dirhams?

dinars

or .. quirats?

quirats

.. or something of that kind? And what if the repetitions relate directly to standard measures of some sort.  As I said, this post is just notes and some musings.

_______________

NOTES

[1]   … as we learn from an inscription on  folio 1r.

[2] Paul Kunitzsch, A new manuscript of Abu Bakr al-Hassar’s Kitāb al-Bayan’.  The same paper was published in  Suhayl No.3 (2003) pp. 187–192.  Note that Kunitzsch refers to the numerals appearing on  “folio 5” but today the Penn website has it as “folio 4r”.

[3] The point is  important given the close comparison between the ‘Gemini’ image and the style informing the Voynich ‘nymphs’. Thus Langerman writes:

The drawings of the constellations …obviously follow the style of those which accompanied the catalogue of al-Sufi. Thus at first glance they could derive from an Arabic copy of al-Sufi, from an Islamic celestial globe (the figures on such globes usually follow those found in the manuscript tradition of al-Sufi’s work), or from a manuscript belonging to the Sufi latinus corpus.  Now al-Sufi provided in his book two drawings for each constellation, one as seen in the sky, and another as seen on the celestial globe (where the left and right sides are always interchanged against their appearance in the sky). The Sufi latinus corpus consistently chooses only one of these illustrations, the view as seen on the celestial globe for sixteen of the constellations, and the view as seen in the sky for the remaining thirty-two. All but five of the drawings found in Sassoon 823 show the figures as seen in the sky; the five which give the representation as seen on the globe are Ophiuchus, Serpens, Equuleus, Andromeda, and Canis Minor. From these considerations it would seem that the figures found in the Sassoon manuscript cannot have been copied from a manuscript of the Sufi latinus corpus, and equally not from an Islamic celestial globe. The only remaining possibility is that they were selected and copied from an Arabic [Persian or other] manuscript of al-Sufi’s treatise. (pp.277-8)
Karl A. F. Fischer, Paul Kunitzsch and Y. Tzvi Langermann. ‘The Hebrew Astronomical Codex MS. Sassoon 823’,   The Jewish Quarterly Review, New Series, Vol. 78, No. 3/4 (Jan. – Apr., 1988), pp. 253-292.

[4] Francesco di Marco Datini, of whom I’ve spoken  before.

[5] Eva Mira Grob, Documentary Arabic Private and Business Letters on Papyrus: Form and Function, Content and Context.  (2010)

As a further note for the mathematicians –  there is a good short paper which sets al-Hassar’s work in context:

Jeffrey A.Oaks and Haitham M. Alkhateebi, ‘Māl, enunciations, and the prehistory of Arabic algebra’, Historia Mathematica, Volume 32, Issue 4, November 2005, pp. 400–425.  Available online through Science Direct (here).

 

 

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